A user has for some time been leaving unpleasant bullying comments. This is not acceptable behaviour. Please ask the user to stop.
If you're being bullied by a regular user, flag the comments and moderators will intervene.
If you're concerned about a moderator rather than a regular user, you may still raise a flag; moderators will not handle flags about their own activity.
If you're concerned about them being aware of it, or need additional help beyond what the moderation team can or will provide, email the StackExchange staff (the 'Contact Us' link below this page), or email a specific staff member (Tim Post and Jon Ericson have been involved before here, I believe; or others from the Communities section on this page). Their emails are generally first initial last name @ stackexchange.com and/or @stackoverflow.com, and the two I mentioned above at least post their email in their public profile. They also are very responsive.
If you're concerned about particular behavior, and wish to constructively and publicly engage the community about that, then a post on meta is welcome and appropriate, with sufficient details to be useful.
If you think you are being bullied, the recourse available to you is to flag the offending comments for moderator action. You can also ask one or more moderators to participate in a private chat with you.
However, before you do, I suggest you take a few preliminary steps:
Make sure that you really are being subject to inappropriate behavior.
This is a public forum, and people disagree. We have a "be nice" rule, but sometimes people take other people expressing different opinions, or merely disagreeing with their own opinions, as "rude" or "bullying". Someone disagreeing with your opinions, or answers, or comments, is not automatically "bullying".
Make sure you are not contributing to the problem.
Look to your own actions before you bringing a moderator into it. Are you criticizing the person, insulting them, or otherwise being antagonistic? It doesn't matter "who started it". This is a parenting site; we should all be mature enough to recognize our own contributions to arguments. If you're contributing, stop, and leave it alone for a while to see if the offending behavior stops once you disengage. If it does, problem solved.
Compile a list of all offending actions.
Saying "so-and-so is being mean to me!" doesn't really help the moderators. Do some of the leg-work for them, and be very specific about what offended you. Were obscenities used? Were you called derogatory names? Did someone accuse you of repeating yourself? Be specific, identify each comment that's problematic, and give the moderators as much information as possible. It saves them and you time.